graph

name	graph
description	Interactive knowledge graph analysis. Routes natural language questions to graph scripts, interprets results in domain vocabulary, and suggests concrete actions. Triggers on "/graph", "/graph health", "/graph triangles", "find synthesis opportunities", "graph analysis".
version	1.0
generated_from	arscontexta-v1.6
user-invocable	true
context	fork
model	sonnet
allowed-tools	Read, Grep, Glob, Bash
argument-hint	[operation] [target] — operations: health, triangles, bridges, clusters, hubs, siblings, forward, backward, query

Runtime Configuration (Step 0 — before any processing)

Read these files to configure domain-specific behavior:

1. ops/derivation-manifest.md — vocabulary mapping, platform hints

   • Use vocabulary.notes for the notes folder name
   • Use vocabulary.note / vocabulary.note_plural for note type references
   • Use vocabulary.topic_map / vocabulary.topic_map_plural for MOC references
   • Use vocabulary.cmd_reflect for connection-finding command name
   • Use vocabulary.cmd_reweave for backward-pass command name

2. ops/config.yaml — for graph thresholds (MOC size limits, orphan thresholds)

If no derivation file exists, use universal terms (notes, MOCs, etc.).

---

EXECUTE NOW

Target: $ARGUMENTS

Parse the operation from arguments:

• If arguments match a known operation: route to that operation
• If arguments are a natural language question: map to the closest operation (see Interactive Mode)
• If no arguments: enter interactive mode

START NOW. Route to the appropriate operation.

---

Philosophy

The graph IS the knowledge. This skill makes it visible.

Individual {vocabulary.note_plural} are valuable, but their connections create compound value. /graph reveals the structural properties of those connections — where the graph is dense, where it is sparse, where it is fragile, and where synthesis opportunities hide.

Every operation produces two things: findings (what the analysis reveals) and actions (what to do about it). Never dump raw data. Always interpret results with {vocabulary.note} descriptions and domain context. Always suggest specific next steps.

---

Operations

/graph health

Full graph health report: density, orphans, dangling links, coverage.

Step 1: Collect raw metrics

# Count total notes (excluding MOCs)
NOTES_DIR="{vocabulary.notes}"
TOTAL=$(ls -1 "$NOTES_DIR"/*.md 2>/dev/null | wc -l | tr -d ' ')
MOC_COUNT=$(grep -rl '^type: moc' "$NOTES_DIR"/*.md 2>/dev/null | wc -l | tr -d ' ')
NOTE_COUNT=$((TOTAL - MOC_COUNT))

# Count all wiki links
LINK_COUNT=$(grep -ohP '\[\[[^\]]+\]\]' "$NOTES_DIR"/*.md 2>/dev/null | wc -l | tr -d ' ')

# Calculate link density
# Density = actual_links / possible_links
# possible_links = N * (N - 1) for directed graph
echo "Density: $LINK_COUNT / ($NOTE_COUNT * ($NOTE_COUNT - 1))"

# Find orphan notes (zero incoming links)
for f in "$NOTES_DIR"/*.md; do
  NAME=$(basename "$f" .md)
  INCOMING=$(grep -rl "\[\[$NAME\]\]" "$NOTES_DIR"/ 2>/dev/null | grep -v "$f" | wc -l | tr -d ' ')
  [[ "$INCOMING" -eq 0 ]] && echo "ORPHAN: $NAME"
done

# Find dangling links (links to non-existent files)
grep -ohP '\[\[([^\]]+)\]\]' "$NOTES_DIR"/*.md 2>/dev/null | sort -u | while read -r link; do
  NAME=$(echo "$link" | sed 's/\[\[//;s/\]\]//')
  [[ ! -f "$NOTES_DIR/$NAME.md" ]] && echo "DANGLING: $NAME"
done

# MOC coverage: % of notes appearing in at least one MOC's Core Ideas
COVERED=0
for f in "$NOTES_DIR"/*.md; do
  NAME=$(basename "$f" .md)
  # Skip MOCs themselves
  grep -q '^type: moc' "$f" 2>/dev/null && continue
  # Check if any MOC links to this note
  if grep -rl '^type: moc' "$NOTES_DIR"/*.md 2>/dev/null | xargs grep -l "\[\[$NAME\]\]" >/dev/null 2>&1; then
    COVERED=$((COVERED + 1))
  fi
done
echo "Coverage: $COVERED / $NOTE_COUNT"

If graph helper scripts exist in ops/scripts/graph/, use them instead of inline analysis:

• ops/scripts/graph/link-density.sh for density metrics
• ops/scripts/graph/orphan-notes.sh for orphan detection
• ops/scripts/graph/dangling-links.sh for dangling link detection

Step 2: Interpret and present

--=={ graph health }==--

  {vocabulary.note_plural}: [N] (plus [M] {vocabulary.topic_map_plural})
  Connections: [N] (avg [X] per {vocabulary.note})
  Graph density: [0.XX]
  {vocabulary.topic_map} coverage: [N]% of {vocabulary.note_plural} appear in at least one {vocabulary.topic_map}

  Orphans ([N]):
    - [[orphan name]] — [description from YAML]
    → Suggestion: Run /{vocabulary.cmd_reflect} to find connections

  Dangling Links ([N]):
    - [[missing name]] — referenced from [[source note]]
    → Suggestion: Create the {vocabulary.note} or remove the link

  {vocabulary.topic_map} Sizes:
    - [[moc name]]: [N] {vocabulary.note_plural} [OK | WARN: approaching split threshold | WARN: consider merging]

  Overall: [HEALTHY | NEEDS ATTENTION | FRAGMENTED]

Density benchmarks:

Density	Interpretation
< 0.02	Sparse — {vocabulary.note_plural} exist but connections are thin
0.02-0.06	Healthy — growing network with meaningful connections
0.06-0.15	Dense — well-connected, watch for over-linking
> 0.15	Very dense — verify connections are genuine, not noise

/graph triangles

Find synthesis opportunities — open triadic closures where A links to B and A links to C, but B does not link to C.

Step 1: Build adjacency data

# For each note, extract outgoing wiki links
for f in "$NOTES_DIR"/*.md; do
  NAME=$(basename "$f" .md)
  LINKS=$(grep -oP '\[\[([^\]]+)\]\]' "$f" 2>/dev/null | sed 's/\[\[//;s/\]\]//' | sort -u)
  echo "FROM:$NAME"
  echo "$LINKS" | while read -r target; do
    [[ -n "$target" ]] && echo "  TO:$target"
  done
done

If ops/scripts/graph/find-triangles.sh exists, use it directly.

Step 2: Find open triangles

For each note A with outgoing links to B and C:

1. Check if B links to C (in either direction)
2. Check if C links to B (in either direction)
3. If neither link exists: this is an open triangle (synthesis opportunity)

Step 3: Evaluate and rank

For each open triangle:

1. Read descriptions of BOTH unlinked {vocabulary.note_plural}
2. Assess: is there a genuine conceptual relationship that the common parent suggests?
3. Rank by potential value: how surprising and useful would the connection be?

Step 4: Present top findings

--=={ graph triangles }==--

  Found [N] synthesis opportunities — pairs of {vocabulary.note_plural} that share
  a common reference but do not reference each other:

  1. [[note B]] and [[note C]]
     Common parent: [[note A]]
     B: "[description]"
     C: "[description]"
     → These may benefit from a connection because [specific reasoning
        about WHY B and C might relate through A's lens]
     → Action: Run /{vocabulary.cmd_reflect} on [[note B]] to evaluate

  2. [[note D]] and [[note E]]
     Common parent: [[note F]]
     ...

  [Show top 10. If more exist: "[N] more triangles found. Show all? (yes/no)"]

Filter out trivial triangles: Skip pairs where:

• Both are in the same {vocabulary.topic_map} (they may already be related through the MOC without direct links)
• One is a {vocabulary.topic_map} itself (MOCs link to everything, triangles with MOCs are noise)
• The descriptions suggest no conceptual overlap

/graph bridges

Identify structurally critical {vocabulary.note_plural} whose removal would disconnect graph regions.

Step 1: Build adjacency list

Build a bidirectional adjacency list from all wiki links in {vocabulary.notes}/.

If ops/scripts/graph/find-bridges.sh exists, use it directly.

Step 2: Find bridge nodes

A bridge note is one where:

• Removing it (and its links) would split a connected component into two or more components
• It is the SOLE connection between clusters of {vocabulary.note_plural}

Implementation: For each note, temporarily remove it and check if the remaining graph has more connected components.

Step 3: Present findings

--=={ graph bridges }==--

  Found [N] bridge {vocabulary.note_plural} — structurally critical nodes whose
  removal would disconnect graph regions:

  1. [[bridge note]] — connects [N] {vocabulary.note_plural} on one side to [M] on the other
     Description: "[description]"
     Cluster A: [[note1]], [[note2]], ...
     Cluster B: [[note3]], [[note4]], ...
     → Risk: If this {vocabulary.note} becomes stale, [N+M] {vocabulary.note_plural}
       lose their connection path
     → Action: Consider adding parallel connections between the clusters

  [If no bridges: "No bridge notes found. The graph has redundant paths between
   all connected regions. This is healthy."]

/graph clusters

Discover connected components and topic boundaries.

Step 1: Build adjacency list

Build a bidirectional adjacency list from all wiki links.

If ops/scripts/graph/find-clusters.sh exists, use it directly.

Step 2: Find connected components

Use BFS/DFS to find all connected components:

1. Start with any unvisited note
2. Traverse all reachable notes via wiki links (bidirectional)
3. Mark as one component
4. Repeat until all notes visited

Step 3: Analyze clusters

For each cluster:

• Size (number of {vocabulary.note_plural})
• Key {vocabulary.note_plural} (highest link count within cluster)
• Topic coverage (which {vocabulary.topic_map_plural} are represented)
• Isolation level (how many links cross cluster boundaries)

Step 4: Present findings

--=={ graph clusters }==--

  Found [N] connected components:

  Cluster 1: [size] {vocabulary.note_plural}
    Key nodes: [[note1]] (8 links), [[note2]] (6 links)
    Topics: [[topic A]], [[topic B]]
    Cross-cluster links: [N]
    → This cluster is [well-connected | isolated | a hub]

  Cluster 2: [size] {vocabulary.note_plural}
    ...

  Isolated {vocabulary.note_plural} ([N]):
    - [[isolated note]] — [description]
    → Action: Run /{vocabulary.cmd_reflect} to find connections

  [If 1 cluster: "All {vocabulary.note_plural} are in one connected component.
   The graph is fully connected. This is healthy."]

/graph hubs

Rank {vocabulary.note_plural} by influence — most-linked-to (authorities) and most-linking-from (hubs).

Step 1: Count links

# Authority score: incoming links per note
for f in "$NOTES_DIR"/*.md; do
  NAME=$(basename "$f" .md)
  INCOMING=$(grep -rl "\[\[$NAME\]\]" "$NOTES_DIR"/ 2>/dev/null | grep -v "$f" | wc -l | tr -d ' ')
  echo "AUTH:$INCOMING:$NAME"
done | sort -t: -k2 -rn | head -10

# Hub score: outgoing links per note
for f in "$NOTES_DIR"/*.md; do
  NAME=$(basename "$f" .md)
  OUTGOING=$(grep -oP '\[\[[^\]]+\]\]' "$f" 2>/dev/null | wc -l | tr -d ' ')
  echo "HUB:$OUTGOING:$NAME"
done | sort -t: -k2 -rn | head -10

If ops/scripts/graph/influence-flow.sh exists, use it directly.

Step 2: Identify synthesizers

Synthesizer {vocabulary.note_plural} score high on BOTH metrics — they absorb many inputs (high authority) and produce many outputs (high hub). These are the most structurally important {vocabulary.note_plural} in the graph.

Step 3: Present findings

--=={ graph hubs }==--

  Top Authorities (most-linked-to):
    1. [[note]] — [N] incoming links — "[description]"
    2. [[note]] — [N] incoming links — "[description]"
    ...

  Top Hubs (most-linking-from):
    1. [[note]] — [N] outgoing links — "[description]"
    2. [[note]] — [N] outgoing links — "[description]"
    ...

  Synthesizers (high on both — structurally important):
    1. [[note]] — [N] in / [M] out — "[description]"
    ...

  [If no clear synthesizers: "No notes score high on both metrics.
   This suggests the graph has separate input and output layers."]

/graph siblings [[topic]]

Find unconnected {vocabulary.note_plural} within a topic — {vocabulary.note_plural} sharing the same {vocabulary.topic_map} but not linking to each other.

Step 1: Read the specified {vocabulary.topic_map}

Find and read the {vocabulary.topic_map} matching the argument. Extract all {vocabulary.note_plural} linked in Core Ideas.

Step 2: Check pairwise connections

For each pair of {vocabulary.note_plural} in the {vocabulary.topic_map}:

1. Does A link to B? (grep for [[B]] in A's file)
2. Does B link to A? (grep for [[A]] in B's file)
3. If neither: this is an unconnected sibling pair

If ops/scripts/graph/topic-siblings.sh exists, use it with the topic argument.

Step 3: Evaluate pairs

For each unconnected pair:

• Read both descriptions
• Assess whether a connection SHOULD exist
• Rate as: likely connection, possible connection, appropriately separate

Step 4: Present findings

--=={ graph siblings: [[topic]] }==--

  {vocabulary.topic_map} [[topic]] has [N] {vocabulary.note_plural}.
  Found [M] unconnected sibling pairs:

  Likely connections:
    1. [[note A]] and [[note B]]
       A: "[description]"
       B: "[description]"
       → [Why these likely relate]

  Possible connections:
    2. [[note C]] and [[note D]]
       ...

  Appropriately separate: [N] pairs — no connection needed

  → Action: Run /{vocabulary.cmd_reflect} on the "likely" pairs

/graph forward [[note]] [depth]

N-hop forward traversal from a {vocabulary.note}. Default depth: 2.

Step 1: Start from the specified {vocabulary.note}

Read the {vocabulary.note} and extract all outgoing wiki links (hop 1).

If ops/scripts/graph/n-hop-forward.sh exists, use it with the note and depth arguments.

Step 2: Traverse

For each linked {vocabulary.note}:

1. Read it and extract its outgoing wiki links (hop 2)
2. Continue to specified depth
3. Track visited notes to avoid cycles

Step 3: Present as annotated tree

--=={ forward traversal: [[note]] (depth [N]) }==--

  [[root note]] — "[description]"
    ├── [[link 1]] — "[description]"
    │   ├── [[link 1a]] — "[description]"
    │   └── [[link 1b]] — "[description]"
    ├── [[link 2]] — "[description]"
    │   └── [[link 2a]] — "[description]"
    └── [[link 3]] — "[description]"

  Reached [N] {vocabulary.note_plural} in [depth] hops.
  Dead ends (no outgoing links): [[note X]], [[note Y]]
  Cycles detected: [[note]] → ... → [[note]] (skipped)

/graph backward [[note]] [depth]

N-hop backward traversal to a {vocabulary.note}. Default depth: 2.

Step 1: Start from the specified {vocabulary.note}

Find all notes that link TO this {vocabulary.note} (hop 1).

NAME="[note name]"
grep -rl "\[\[$NAME\]\]" "$NOTES_DIR"/*.md 2>/dev/null

If ops/scripts/graph/recursive-backlinks.sh exists, use it with the note and depth arguments.

Step 2: Traverse backward

For each linking {vocabulary.note}:

1. Find what links to IT (hop 2)
2. Continue to specified depth
3. Track visited notes to avoid cycles

Step 3: Present as annotated tree

--=={ backward traversal: [[note]] (depth [N]) }==--

  [[root note]] — "[description]"
    ├── [[referrer 1]] — "[description]"
    │   ├── [[referrer 1a]] — "[description]"
    │   └── [[referrer 1b]] — "[description]"
    ├── [[referrer 2]] — "[description]"
    │   └── [[referrer 2a]] — "[description]"
    └── [[referrer 3]] — "[description]"

  [N] {vocabulary.note_plural} lead to [[root note]] within [depth] hops.
  Entry points (no incoming links): [[note X]], [[note Y]]

/graph query [field] [value]

Schema-level YAML query across {vocabulary.note_plural}.

Step 1: Parse field and value

Supported query patterns:

Query	Ripgrep Pattern	Purpose
topics [[X]]	rg '^topics:.*\[\[X\]\]'	Find notes in a topic
type tension	rg '^type: tension'	Find notes by type
methodology X	rg '^methodology:.*X'	Find notes by tradition
status open	rg '^status: open'	Find notes by status
created 2026-02	rg '^created: 2026-02'	Find notes by date range
source [[X]]	rg '^source:.*\[\[X\]\]'	Find notes from a source

Step 2: Execute query

rg "^{field}:.*{value}" "$NOTES_DIR"/*.md -l 2>/dev/null

For each matching file, extract the description for context.

Step 3: Present results

--=={ graph query: {field} = {value} }==--

  Found [N] {vocabulary.note_plural}:

  1. [[note name]] — "[description]"
  2. [[note name]] — "[description]"
  ...

  Distribution:
    [If querying topics: how many per sub-topic]
    [If querying type: breakdown by status]
    [If querying methodology: breakdown by tradition]

---

Interactive Mode

If no arguments provided:

1. Ask: "What would you like to know about your knowledge graph?"
2. Map natural language to operation:

User Says	Maps To	Why
"Where should I look for connections?"	triangles	Finding synthesis opportunities
"What are my most important notes?"	hubs	Authority/hub ranking
"Are there isolated areas?"	clusters	Connected component detection
"How healthy is my graph?"	health	Full health report
"What bridges my topics?"	bridges	Bridge note identification
"What connects to [[X]]?"	backward [[X]]	Backward traversal
"Where does [[X]] lead?"	forward [[X]]	Forward traversal
"Show me notes about [topic]"	query topics [[topic]]	Schema query
"What needs connecting in [topic]?"	siblings [[topic]]	Unconnected sibling pairs

3. Run the mapped operation
4. After presenting results, offer follow-up: "Want to explore any of these further?"

---

Output Rules

• Never dump raw data. Always interpret results with {vocabulary.note} descriptions and context.
• Always suggest actions. "Run /{vocabulary.cmd_reflect} on these pairs" or "Consider adding a bridge {vocabulary.note} about X."
• Use domain vocabulary for all labels and descriptions — {vocabulary.note}, {vocabulary.topic_map}, etc.
• For large result sets, summarize top findings (max 10) and offer to show more: "[N] more results. Show all? (yes/no)"
• Include density benchmarks for context — "your density of 0.04 is in the healthy range."
• Distinguish structural from semantic. Graph analysis reveals structural properties. Semantic judgment about WHETHER connections should exist requires /{vocabulary.cmd_reflect}.

---

Edge Cases

Small Vault (<10 notes)

Report metrics but contextualize: "With [N] {vocabulary.note_plural}, graph analysis provides limited insight. Graph operations become more valuable as the knowledge graph grows. Current metrics are baseline measurements."

All operations still run — they just produce less data.

No Graph Scripts Available

If ops/scripts/graph/ does not exist or individual scripts are missing, implement the analysis inline using grep, file reads, and bash loops as shown in each operation's steps. The inline implementations are complete — scripts are optimization, not requirements.

No ops/derivation-manifest.md

Use universal vocabulary (notes, MOCs, etc.). All operations work identically.

Empty Notes Directory

Report: "No {vocabulary.note_plural} found in {vocabulary.notes}/. Start by capturing content to build your knowledge graph."

Note Not Found (for forward/backward/siblings)

If the specified {vocabulary.note} or {vocabulary.topic_map} does not exist:

1. Search for partial matches: ls "$NOTES_DIR"/*{query}*.md 2>/dev/null
2. If matches found: "Did you mean: [[match1]], [[match2]]?"
3. If no matches: "{vocabulary.note} '[[name]]' not found. Check the name and try again."